1. Field of the Invention
This invention relates generally to crossover filters for use with multi-way loudspeaker systems with non-coincident drivers.
2. Related Art
Crossover filters used in multi-way loudspeaker systems having non-coincident drivers are designed to effectively divide the frequency band into partitions, so that the individual drivers work within the frequency bands for which they were designed, so that distortion is minimized. At the same time, it is highly desirable for the resulting acoustic frequency responses of the whole loudspeaker system to be reasonably flat or smooth within an area, not only at a single point in space. Typically, it has not been possible to achieve a reasonable flat or smooth frequency response within an area due to the required spacing between the drivers. Drivers typically have to be spaced apart due to their physical size. The amount of required spacing usually compares with the wavelength of the radiated sound. This required physical spacing causes interferences due to different path lengths of sound waves traveling from the drivers to the considered point in space. Attempts have been made to address these problems; however, past attempts have not overcome all disadvantages.
By way of example, FIG. 1 illustrates a typical, four-way loudspeaker that is known in the art. The four drivers are connected to four crossover filters H0, . . . , H3. The first driver D0 has a membrane diameter of approximately 0.015 m and is located at the origin x0 of the loudspeaker. The second driver D1 employs a membrane of approximately 0.030 m in diameter and is located at x1=0.06 m. The third driver D2 measures approximately 0.11 m in membrane diameter and is located at x2=0.17 m, while the forth driver D3 is approximately 0.30 m in membrane diameter and located at x3=0.40 m.
One known and suggested filtering method for use in multi-way loudspeakers, such as the prior art loudspeaker illustrated in FIG. 1, is the 4th order “Linkwitz-Riley” crossover filters. FIG. 2 illustrates the frequency response of 4th order Linkwitz-Riley crossover filters H0, . . . , H3 employed in prior art loudspeaker illustrated in FIG. 1. As employed with the prior art drivers shown in FIG. 1, the crossover frequencies would be typically 100 Hz, 600 Hz, and 2500 Hz, as illustrated by FIG. 2. The filters may be implemented both as analog or digital filters. To determine the acoustic frequency responses of the loudspeaker using 4th order Linkwitz-Riley crossover filters, a model employing ideal flat, circular membranes and pistonic motion, may be used. The frequency responses may be determined at vertical displacement angles of 0 to 45 degrees (0 . . . 45) in 5 degree steps, simulated upward and downward, respectively, relative to the main axis which is perpendicular to x=0.
FIG. 3 illustrates the resulting frequency responses, at vertical displacement angles 0 . . . 45 degrees in 5 degree steps, simulated positive upwards relative to the main axis which is perpendicular to x=0. FIG. 4 illustrates the resulting frequency responses, at vertical displacement angles 0.45 degrees in 5 degree steps, simulated negative downwards relative to the main axis which is perpendicular to x=0. As illustrated by FIGS. 3 & 4, the simulation illustrates that interferences around the crossover points cause large deviations from the desired flat response curves out of the main axis. Thus, employing the 4th order Linkwitz-Riley crossover filters does not achieve the desired flat frequency responses over the area of interest.
More recently, the use of 4th order Chebychev filters has been recommended with a prescribed stopband attenuation and flat passband. FIG. 5 illustrates the frequency responses of prior art 4th order “Chebychev Notched” crossover filters H0, . . . , H3 with a stopband attenuation of 30 db and flat passband employed in the prior art loudspeaker of FIG. 1. Applying the Chebychev filters to the prior art loudspeaker of FIG. 1 with a stopband attenuation of 30 db, the simulated frequency responses also reveal problems with the use of the 4th order Chebychev filters. FIG. 6 illustrates the resulting frequency responses, at vertical displacement angles 0 . . . 45 degrees in 5 degree steps, simulated positive upwards relative to the main axis which is perpendicular to x=0. FIG. 7 illustrates the resulting frequency responses, at vertical displacement angles 0 . . . 45 degrees in 5 degree steps, simulated negative downwards relative to the main axis which is perpendicular to x=0. As illustrated by FIGS. 6 & 7, although the error regions are narrowed and thus less audible, deviation still exists around the cross over points and thus does not achieve the desired flat frequency responses over the desired area.
Yet another alternative is to use digital, linear phase finite impulse response (“FIR”) filters with very narrow transition bands. FIG. 8 illustrates the frequency responses of digital, linear phase FIR filters H0, . . . , H3 with very narrow transition bands employed in the prior art loudspeaker of FIG. 1. By applying FIR filters to the FIG. 1, prior art loudspeaker, it is determined by simulating the measured frequency response of these filters that the upward and downward responses are now identical, because the filters introduce no phase distortion. Additionally, the widths of the transition regions are also minimized. However, the directivity characteristics of the individual drivers result in non-uniform out-of-axis frequency responses. These shortfalls are demonstrated by FIG. 9 which illustrates the simulated acoustic far field frequency responses at vertical angles 0 . . . 45 degrees in 5 degree steps, upwards and downwards with respect to tweeter axis, using crossover filters of FIG. 8.
Finally, d'Appolito proposes a symmetric arrangement of two midrange drivers around a center tweeter to reduce lobing errors. To employ d'Appolito's proposal the prior art loudspeaker illustrated in FIG. 1 must be extended, as illustrated in FIG. 10, to have a center tweeter at x0, two first midranges at +/−x1, two further woofer/midranges at +/−x2, and two woofers at +/−x3 symmetrically arranged with respect to the center tweeter at x0. FIG. 11 illustrates the frequency responses of the crossover filters H0, . . . , H3 using 3rd order Butterworth crossover filters as suggested by d'Appolito with the symmetric arrangement illustrated in FIG. 11. FIG. 12 illustrates the simulated acoustic far field frequency responses at vertical angles 0 . . . 45 degrees in 5 degree steps, upwards and downwards with respect to tweeter axis, using loudspeaker system of FIG. 10 and crossover filters of FIG. 11. As illustrated by FIG. 12, the loudspeaker system now becomes directive over larger frequency bands, which is desirable in most cases; however, the directivity is not constant over frequency.
Therefore, a need exists for a filtering method and systems for use with multi-way loudspeakers that are designed to effectively divide the frequency band into partitions, so that distortion is minimized and that also produce resulting acoustic frequency responses that are reasonably flat or smooth within an area, thus overcoming the disadvantages set forth above and others previously experienced.